Therefore, in order to make quantitative progress, it is necessary to track the evolution of \(\left<\mathbf {E}\cdot \mathbf {B}\right>\)  during axion inflation all the way to its end.
This, however, represents a technical challenge because of the highly nonlinear interplay of fermion and gauge-field production.
In the following, we will therefore discuss several different estimates for the efficiency of gauge-field production during axion inflation that have recently been put forward in the literature.
A more detailed discussion of these estimates, including semianalytical fit functions that describe the exact numerical results with excellent accuracy, can be found in Ref. [1]}.
